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人気のある微分積分 >

integral from 1 to 2.2 of x^3e^{x+1}

解

\int_{1}^{2.2} x^{3} e^{x + 1} d x

解

96.42237 \dots

解答ステップ

\int_{1}^{2.2} x^{3} e^{x + 1} d x

x^{3} e^{x + 1} = e^{1} x^{3} e^{x}

= \int_{1}^{2.2} e^{1} x^{3} e^{x} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{1} \cdot \int_{1}^{2.2} x^{3} e^{x} d x

簡素化

= e \cdot \int_{1}^{2.2} x^{3} e^{x} d x

部分積分を適用する

= e [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{1}^{2.2}

\int 3 x^{2} e^{x} d x = 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

= e [x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))]_{1}^{2.2}

限度を計算する:

35.47180 \dots

= e 35.47180 \dots

簡素化

= 96.42237 \dots

グラフ

人気の例

integral from 0 to 1 of (4x)/(1+x^2)

\int_{0}^{1} \frac{4 x}{1 + x ^{2}} d x

integral from 2 to 3 of (3x)/(1+x^2)

\int_{2}^{3} \frac{3 x}{1 + x ^{2}} d x

integral from 1 to 3 of 1/(4x)

\int_{1}^{3} \frac{1}{4 x} d x

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\int_{- 1}^{2} x^{2} + x + 2 d x

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\int_{- 1}^{5} cos (x) d x